Ed Miliband has said he supports the reform of prime minister's questions, suggesting the atmosphere makes viewers believe their children are better behaved than politicians.

Backing John Bercow, the Speaker of the Commons, who condemned the "twittish" behaviour of MPs, the Labour leader said he would like to reach a cross-party deal to change the format of the weekly sessions.

Successive party leaders, including David Cameron and Miliband, have said they want to make the tone of prime minister's questions less combative. However, Miliband's attempts to introduce a more measured tone to the exchanges have met with limited success as MPs on all sides continue to bellow and heckle.

Bercow has written to the prime minister to seek talks with the party leaders on how the weekly Wednesday sessions can be improved.

In an interview last week he said: "There are people who think culturally the atmosphere is very male, very testosterone-fuelled and, in the worst cases, of yobbery and public school twittishness."

Miliband told the BBC's World This Weekend that he fully supported the Speaker's position. "I think it subtracts from the reputation of politics," he said. "I think lots of previous leaders, not just of the Labour party, but of the Conservative party would say that too. It's easy to say it's a problem, it's harder to change it, but I'm totally up for finding ways to change it …

"We should endeavour to be proud of the show we put on for the country, not giving people a sense that their kids behave better than we do."

Miliband is setting out his plans to engage more people in politics by allowing them to become affiliated Labour members for just £3 and gain a vote on future leaders. Full members, who will pay much more, will have the right to vote on parliamentary candidates.

He is targeting around 200,000 new members – doubling the current number – following the reforms, which he described as the biggest change to the party's structure since it was founded in 1918.

As part of the reforms introduced in the aftermath of the Falkirk "vote-rigging" scandal, trade union members will have to opt in to paying membership fees to the party, rather than levies being automatically taken.

The reforms, due to be passed at a special conference next month, were this weekend backed by Lord Adonis, a senior Labour figure, who said it would open the party up to people from all walks of life.